For complex coupled processes a non-intrusive ROM is attractive because it does not require any cumbersome modifications of FOM source codes [1]}, [2]}, [3]}, [4]}, [5]}. This alleviates several code compatibility complications since many of the source codes used to build FOMs may not be available or easily accessible, especially in legacy codes or commercial software [6]}. Consequently, the non-intrusive variants of ROM can provide more flexibility in coupling to any existing FOM platforms. We focus on two ways of building a ROM; the first path in, the linear approach, follows the recent development of [4]}, which has been adapted and applied to a wide range of problems [8]}, [9]}, [10]}, [11]}, [12]}. This approach utilizes a set of reduced basis functions, which are linearly extracted from high-fidelity FOM solutions through proper orthogonal decomposition (POD). Then, the ROM solution, which belongs in a linear subspace of the solution manifold, is reconstructed from these reduced basis functions. In the second path, the nonlinear approach, we propose the compression of the high-fidelity FOM solutions through an autoencoder (AE in short) [13]}, [14]}, [15]}, [16]}, [17]}, [18]} learning a nonlinear manifold for the ROM solution. During the prediction phase, we reconstruct our ROM using nonlinear reconstruction (i.e., using a trained decoder to reconstruct our quantities of interest with a given nonlinear manifold). We want to emphasize that in contrast to the work presented in [13]}, [15]}, [17]}, our framework relies on the non-intrusive approach similar to [16]}, [18]}, which avoids any intrusive modifications of FOM source code. This type of non-intrusive approach for ROM using AE is termed Deep-Learning ROM (DL-ROM) by [18]}. Hence, the framework could be easily extended to other engineering problems. This work has three main novelties
